If the roots of the equation x^2 + bx + c = 0 | vedclass

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(C) Let the roots of the quadratic equation $x^2 + bx + c = 0$ be $\alpha$ and $\frac{1}{\alpha}$.According to the properties of quadratic equations,t

Vedclass · Accepted Answer

$a = c$

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(C) Let the roots of the quadratic equation $x^2 + bx + c = 0$ be $\alpha$ and $\frac{1}{\alpha}$.According to the properties of quadratic equations,the product of the roots is given by $\frac{c}{a}$.Here,the equation is $1x^2 + bx + c = 0$,so $a = 1$.The product of the roots is $\alpha 	imes \frac{1}{\alpha} = 1$.Therefore,$\frac{c}{a} = 1$.Since $a = 1$,we get $c = 1$.Looking at the options,if $a = c$,then $1 = c$,which is consistent with our result. Thus,$a = c$ is the correct condition.

If the roots of the equation $x^2 + bx + c = 0$ are reciprocals of each other,then...

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